The purpose of a solenoid is so that the switch is carrying only signal amperage--a tenth of an amp or so-- while the actual power amperage is directed to the motor. It is safer
The difference in solenoids is the size of the power carrying contacts and their material. For example: Outboard power trim solenoids are 12 volt and have a capacity of about 30 amps. The internal contact points are about the size of the contacts of a set of automotive points--say 3/16 inch diameter and about 1/8 inch thick. Starter motor solenoids are also 12 volts but the internal contacts are much beefier. They range about 3/8 diameter by about 3/16 thick and are probably rated for around 200 amps. Some industrial solenoids have silver contacts, increasing the current carrying capacity due to silver's superior conductivity. These have contacts well over 1/2 inch diameter and are rated for fork-truck used at 48 volts. They are extremely expensive.
Without knowing the size of the motor on the winch it is difficult to describe what solenoid to buy. If you do not have a wiring harness or specifications it would be best to email the company for a solenoid recommendation. At minimum, they should know the amp draw of the winch motor,
Since it is not a starter motor or other heavy duty application, I suspect that it draws about 30 amps like a trailer electric winch. You can also check in the local auto store or catalog and see what bumper mount winches draw in amps..